On the Decay Rate of the False Vacuum

TL;DR

This paper develops a finite size theory of metastability in a quartic potential using semiclassical path integrals, revealing how size and temperature influence the decay rate of the false vacuum.

Contribution

It introduces a finite size approach to metastability, connecting temperature, size, and quantum effects, and computes the ground state lifetime deviations from infinite size theory.

Findings

Ground state lifetime deviates significantly from infinite size predictions.

Temperature effects on fluctuation spectrum are quantitatively evaluated.

Eigenvalues related to metastability are determined as functions of size and temperature.

Abstract

The finite size theory of metastability in a quartic potential is developed by the semiclassical path integral method. In the quantum regime, the relation between temperature and classical particle energy is found in terms of the first complete elliptic integral. At the sphaleron energy, the criterion which defines the extension of the quantum regime is recovered. Within the latter, the temperature effects on the fluctuation spectrum are evaluated by the functional determinants method and computed. The eigenvalue which causes metastability is determined as a function of size/temperature by solving a Lam\`{e} equation. The ground state lifetime shows remarkable deviations with respect to the result of the infinite size theory.